LIBRARY OF CONGRESS. 



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Shelf .:p3.~- 

ENITED STATES OF AMERICA. 






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TO ACCOMPANY THE 

Containing a Complete Course 

— OF— 

pokleirjs 0:1)0. lllusfpafiorjs 

OF THE 

FUNDAMENTAL PRINCIPLES 

*JrLl FOR THE USE OF 

leadiers, {Schools 1 Families, 

Rev. JOHN DAVIS, A>«^" •'"''' 

AUTHOR OF THE 'ELEMENTS OF ASTRONOMY," 
ALLEGHENY CITY, PA. 



Entered according to Act of Congress, in the year 1884, by 

JOHN DAVIS, 
in the Office of the Librarian of Congress, at Washington. 



l> 



PREFACE. 

The object of this Manual is to conduct and aid pupils by a 
brief, easy and natural way in obtaining a correct knowledge of 
the Principles of Geography. Its pages are not multiplied, as 
is frequently the case, with matter that properly belongs in gen- 
eral text books, but are confined to presentations and illustra- 
tions of the elements of the subject under consideration. It 
leads the pupil step by step to consider and observe by practical 
demonstrations on a Terrestrial Globe, how the principles of 
Geography are related and combined, so as to form the basis of 
the Ssienci. The spherical shape of the Globe itself, and all of 
the natural divisions of the Earth having their counterparts 
marked on the map that covers it, tend to this end, so also do 
the lines and circles which are drawn thereon, whereby distan- 
ces may be measured and places located and described. The 
Essentials of the Science being grouped together on the Globe 
in their proper relations,- The Manual presents a comprehensive 
series of Problems and Examples whereby the pupil may have a 
vivid exemplification of their meaning, and thereby arrive at 
the full measure of that instruction which underlies this de- 
partment of mental culture. 



EXPLANATIONS. 



The Author while preparing this Manual, carefully consult- 
ed the best English, French and American Authorities on the 
use of Globes, with the view of having it simple, brief and at 
the same time sufficiently comprehensive for the purpose for 
which it is designed. 



The Definitions and Explanations which relate to the sub- 
jects considered in this Manual are, for the sake of convenience 
placed after the Illustrations and Problems. And in connec- 
tion with each of the Illustrations and Problems reference is 
given to such Definitions and Explanations as should be studied 
with care before entering upon its solution. 



CONTENTS. 

I. To find the Longitude and Latitude of a given place. 

II. Two places being given, to find their difference of 
Latitude. 

III. To find all places that have the same Latitude or the 
same Longitude with a given place. 

IV. Two places being given, to find their difference of 
Longitude. 

V. The Latitude and Longitude of a place being given, 
to find the place. 

VI. To find the distance between two places. 

VII. To rectify the Globe for any given place. 

VIII. To find the Antceci of a given place. 
IX. To find the Perioeei of a given place. 

X. To find the Antipodes of a given place. 

XI. To find places equally distant from a given place. 

XII. The Latitude of a place, its distance and general direc- 
tion from a given place, being given, to find the 
place whose Latitude is given. 

5 



CONTENTS. 

XIII. The Longitude of a place, its distance and general 

direction from a given place, being given, to find 
the place whose Longitude is given. 

XIV. Any Parallel of Latitude being given, to find how 

many miles make a degree of Longitude on it. 

XV. To find at what rate per hour any point on the 
Earth's surface moves by its axial rotation. 

XVI. To illustrate a Right Sphere. 

XVII. To illustrate a Parallel Sphere. 

XVIII. To illustrate an Oblique Sphere. 

XIX. To find the Sun's place in the Ecliptic on any given 
day in the year. 

XX. To find the Sun's Longitude, Right Ascension and 
Declination for any given day. 

XXI. To find on what two days of the year the Sun will be 
vertical at any given place within the Tropics. 

XXIT. To find the difference of time between any two 
places. 

XXIII. The hour being given at any place on the Earth, to 

determine what hour it is at any other given place. 

XXIV. To find the time of the Sun's Rising and Setting on 

any given day, at a place whose Latitude is given. 

XXV. To find all places where the Sun is vertical on a given 

day. 



CONTEXTS. 

XXVI. The day and hour of the day at any place being 

given, to find where the Sun is vertical at that 
time. 

XXVII. To find the Month and Day of the month, wh-n the 

Sun's place in the Ecliptic is in any given De- 
gree, in any given Sign. 

XXVIII. To find on a given day, those portions of the Earth 

on which the Sun does not rise or set. 

XXIX. At any given place and on any given day of the year, 

to find the length of the day and also of the night. 

XXX. At any given place on any given day of the year, tg, 

find the Sun's Meridian Altitude and Zenith Dis- 
tance. 

XXXI. To find the Sun's Altitude and Zenith Distance, at any 

given hour of any given day, at any given place. 

XXXII. To find the Hour of any given day, at any given place, 

when the Sun's Altitude is given. 

XXXIII. To find the bearing and distance of one place from 

another. 

XXXIV. To find that part of the Globe where the Sun ceases 

to rise, and that part where he ceases to set on 
any given day. 

XXXV. To find when Twilight Begins, Ends and its Dura- 

tion on any given day, at any given place in the 

Torrid or Temperate Zones. 
7 



CONTENTS. 

XXXVI. To find the Sun's Azimuth and Amplitude, at any 

given place for any given hour of any given day. 

XXXVII. The Sun's Amplitude or Azimuth being given at 

any given hour of any given day, to find the 
Latitude of the place of the observer. 

XXXVIII. To ' find at what time tie Sun will be due East 

and due West,at any given place on any given 
day. 

XXXIX. To find that part of the Equation of time or differ- 

ence between Clock and Sun time, which depends 
on the obliquity of the Ecliptic, on any day that 

they do not agree. 

XL. At any given place in the Nor;h Frigid Zone, to 
find the beginning and end of constant day. 

XLI. The Month, Day, and Hour of the day being given at 
any place, to find where the Sun is vertical, and all 
places that have Noon, and all places that have 
Midnight, 

XLII. To find the Sun's Longitude and Declination, by the 
Analemma, for any given day. 

XLIII. To find, by the Analemma, on what two days of the 
year the Sun will be vertical at any given place with- 
in the Tropics. 

XLIV.To find, by th3 Analemma, all places where the San 
will be vertical on a given day. 

8 



CONTEXTS. 

XLV. At any given place in the North Frigid Zone, to" find, 
by the Analemma, the length of the longest day. 

XL VI. Any place being given in the South Frigid Zone, to 
find, by the Analemma, the length of the longest day. 

XLVII. Any place being given in either of the Frigid Zones, 
to find, by the Analemma, the length of 'he longest night. 

XL VIII. The longest and the shortest day in either Hemis- 
phere being given, to find the width of the Tor- 
rid Zone. 

XLIX. The time of the Occurrence of a Lunar Eclipse, in 
the mean Solar Time of any place, being given, and 
its duration, to find those parts of the Earth where 
the beginning and end of the Eclipse are visible, 
also those regions where the Eclipse is visible 
throughout its duration. 

L. The time of the Occurrence of a Solar Eclipse, in 
the mean Solar Time of any place, being given, 
and also its duration, to find those regions on the 
Earth in which it is visible. 



STAR GLOBE. 

Letters representing the principal parts of the Star Globe. 
T. The Tripod. I. The Hour Index. S. The Spiral Springs. 
M. The Meridian. m P. The Polar Bearings. 

B. The Meridian Bearing. Q. The Quadrant. 

H. The Horizon. G. The Globe. 

Directions for put tiny the parts together. 
1st. Insert the shaft of the Meridian Bearing B, in the 
socket of the shaft of the Tripod T, and turn the screw in the 
Tripod till it conies in contact with the shaft of the Meridian 
Bearing B. 

'2nd. Drop one of the two Spiral wire-springs S, into each 
end of the tubular axis of the Globe and put the Hour Index 
marked South on the South Pole, and the one marked North 
on the North Pole, and follow the Spiral wire-springs into the 
ends of the tubular axis of the Globe, with the shafts of the 
Polar Bearings P. 

3rd. Place the groove in the outer end of one of these Bear- 
ings, on the inside of the Meridian M, and remove the small 
plate on the end of the other Polar Bearing, with a small screw 
driver, (taking care not to lose the very sma 1 ! rollers through 
which the screws pass.) and press the IN ar Bearing towards 
the center of the Globe till it takes its place on the inside of 
the Meridian M, and then replace the small plate which was re- 
moved from the Polar Bearing, and the Globe is ready for use. 



10 




STAR GLOBE. 



STAR GLOBE. 

(Diameter 12 inches.) 

The Star Globe, being complete in all its appointments, con- 
tains elements of utility and durability which are not 
found in any other. Unlike many others, that are now being 
made without a Graduated Meridian, or Hour Indices, or 
Quadrant of Altitude, or Horizon, it possesses all of these 
parts, and all others which are essential either for convenience 
or instruction. 

GLOBE STAND. 

The Globe is mounted on a metallic Tripod, which is light, 
substantial, convenient, neatly japanned, and tastefully 
ornamented. 

MERIDIAN. 

The Meridian which contains the Globe is brass, plated 
with nickel, and graduated on both sides. One-fourth 
of its circumference is inserted in a concave metallic bearing 
to give it permanence, which bearing is united with the central 
shaft of the Tripod by a Swivel, so that it will revolve hori- 
zontally, without changing tne position of the Tripod. 

HORIZON. 

The Horizon is also composed of metal, and it is so fitted to 
the Meridian at its horizontal diameter, that it may be 
conveniently removed and replaced. Upon it is a 
Map containing the Signs of the Ecliptic and their divisions 

12 



STAR GLOBE. 

into degrees, the Months of thj Year and their divisions into 
Days, the Cardinal and Minor Points of the Compass and the 
degrees of Azimuth and Amplitude. 

• THE GLOBE. 

The Globe itself which is twelve inches in diameter, is con- 
structed of materials that are tough, light, durable and not 
perceptibly effected by any climatic changes of temperature. 
It is skillfully made, which in conjunction with the strength of 
the materials of which it is composed, renders its surface proof 
against change of form unless improperly used. 

GLOBE MAP. 

The Geographical Map with which this Globe is covered is 
issued by the Map Publishing House of W. & A. K. John- 
ston, Edinburgh, Scotland, and this is a sufficient guarantee 
that it has no superior. It is engraved in copper and printed 
in colors, and contains the Ocean Currents, the Isochimal and 
Isothermal lines, the latest Political Divisions and Boundaries 
of all Countries, the corrected Boundaries of the States and 
Territories of the LTnited States, the Topography of various 
places and Countries as reported by modern Explorers, 
together with much new matter which is the outgrowth of 
both National and International enterprise. This array of 
additional knowledge, combined with that which the Map 
originally contained, gives to the Globe which it covers a value 
which many others do not possess. 

13 



STAR GLOBE. 

GLOBE MOVEMENT. 

The Axis of the Globe, unlike all others, is made of metal 
tubing, and in its ends are placed springs and bearings on 
which it revolves. The outer ends of these bearings are 
grooved so as to receive the inner edge of the Meridian, and 
they move on it when a change in the position of the axis of 
the Globe is desired, a novel and very convenient device for 
this purpose. 

HOUR INDICES. 

The Hour Indices, which are placed around the Poles of 
the Globe are stamped out of sheet brass and nickel-plated. 
Each Index is divided into twenty-four equal parts, and these 
parts have associated with them characters that represent the 
hours of the day. 

QUADRANT OF ALTITUDE. 

The Quadrant of Altitude is a flexible strip of metal grad- 
uated into equal parts, each corresponding in length to a de- 
gree on the Globe, and bent when in use so as to closely fit its 
surface. 

THE ANALEMMA. 

The Analemma on the Globe is a diagram which extends 
across the Torrid Zone. It contains the days of each month 
in the year, so arranged, that if the month and day of the 
month are given, the Declination of the Sun at that tinn may 
be readily found, or if the Declination of the Sun is given, 
the month and day of the month may be readily found, and 

14 



STAR GLOBE. 

the Sign and the degree of the Ecliptic in which he is, also, 
the Equation of time, or the difference between Sun and Clock 
time for any day of the year. 

THE STAR GLOBE is manufactured by Skillful 
Mechanics in the most substantial manner, and an 
exact duplicate of any part of it can he obtained at any 
time by applying to the Patentee. 

A Manual containing a comprehensive series of Problems, 
Examples and Illustrations will accompany each Globe. 



15 



PROBLEMS AND EXAMPLES. 
Problem I. 
To find the Longitude and Latitude of any given place. 

See Definitions 46, 48. 

Find the given place on the Globe and adjust the Globe so 
that the Equator is directly under of the Graduated Me- 
ridian, then bring the given place to the Meridian and the de- 
gree expressing the Longitude of the given place is found on 
the Globe directly under and the number of degrees count- 
ed on the Meridian ficm to the given place is its Latitude. 

Note. — For the sake of brevity the word "Meridian" is used instead of 
"Graduated Meridian". 

Examples. 

1. What is the Latitude of the Cape of Good Hope ? 

2. What is the Latitude of St. Pctersburgh ? 

3. What is the Longitude of Pittsburgh ? 

4. What is the Longitude of Calcutta? 

5. What places have the greatest Latitude ? 

6. What places have no Latitude ? 

Problem II. 
Two places being given, to find their difference of Latitude. 

See Definitions 22, 26. 

Find the Latitude of each place by Problem I. and if both 
places are on the same side of the Equator, subtract the less 

16 



PROBLEMS AND EXAMPLES. 

number of degrees of Latitude from the greater and the re- 
mainder will be the difference of Latitude; but if the Lati- 
tude of one of the places is North of the Equator and that 
of the other South of the Equator, add them together and 
their sum will be the difference of Latitude. 

Examples. 

1. What is the difference of Latitude between New 

Orleans and Memphis ? 

2. What is the difference of Latitude between the Tropic 

of Cancer and the Tropic of Capricorn. 

3. What places have the greatest difference of Latitude. 

Problem III. 

To find all those places that have the same Latitude or 
the same Longitude ivith a given place. 

Find the given place on the Globe and adjust the Globe- 
so that of the Meridian is directly over the Equator ; 
then bring the given place to the Meridian and the degree 
expressing the Longitude of the place is found on the Globe 
directly under 0, and all other places having the same Longitude 
will be under the same Meridian, and all other places having the 
same Latitude as that of the given place will pass under the degree 
on the Meridian expressing the Latitude of the given place by 
revolving the Globe once on its axis. 

17 



problems and examples. 
Examples. 

1. What is the Longitude of Lexington ? 

2. What other places have nearly the same Longitude as 

Lexington ? 

3. What is the Longitude of Hong Kong ? 

4. What other places have nearly the same Longitude 

as Hong Kong ? 

5. What places have no Longitude ? 

6. What places have the greatest Longitude ? 

Problem IV. 

Two places being given, to find their difference of Longitude. 

See Definition 21, note 3d, also 26 and notes. 

Find the Longitude of each place by Problem III. and if 
both places are East or both West of the Prime Meridian, sub- 
tract the less number from the greater for the difference of 
Longitude, but if one place is East and the other West of the 
Prime Meridian, add them together and their sum, if it be less 
than 180 degrees, will be the difference of Longitude; if the 
sum exceeds 180 degrees, subtract it from 360 degrees for the 
difference of Longitude. 

Note.— "Prime Meridian" is the Meridian from which Longitude is 
measured East or West, 180 degrees. 

Examples. 
1. What is the difference of Longitude between Con- 
stantinople and Yokohama ? 

18 



PROBLEMS AND EXAMPLES. 

2. What is the difference of Longitude between Wash- 

ington and Madras ? 

3. What is the difference of Longitude between Santa 

Fe and Hong Kong. 

Problem V. 

The Latitude and Longitude of a place being given, to 
find the place. 

Adjust the Globe so that on the Meridian is directly over 
the Equator and revolve the Globe on its axis till the given 
Longitude is under the Meridian; then under the given num- 
ber of degrees of Latitude marked on the Meridian North or 
South is the place required. 

Examples. 

1. Find the Island whose Latitude is 65 degrees North 

and Longitude 20 degrees West. 

2. Find the Island whose Latitude is 42 degrees South 

and Longitude 145 degrees East. 

3. Find the Cape whose Latitude is 56 degrees South and 

Longitude 64 degrees West. 

Problem VI. 
To find the distance between two places. 
Place of the Quadrant over one of the places and extend 
it to the other place and the number of degrees between the 
places will be the distance in degrees, which, multiplied by 60 will 

19 



PROBLEMS AND EXAMPLES. 

give the distance in Geographical miles, or multiplied by 69.1, 
will give the distance in Statute miles. 

Note. — For the sake of brevity, the word Quadrant is used instead of 
"Quadrant of Altitude." 

Examples. 

1. t What is the distance in degrees and in Geographical 

miles between Philadelphia and San Francisco ? 

2. Find the distance in degrees \ between the Falkland 

Islands and the Equator. 

3. What is the distance in degrees from St. Helena to 

Cape Verd, via Monrovia? 

Problem VII. 
To Rectify the Globe for any given place. 

See Definitions 40, 41, 42 and notes. 

Elevate the corresponding Pole as many degrees from the 
Horizon as the given place is distant from the Equator, then 
the Equator and Parallels of Latitude and Circles of Daily Mo- 
tion will have their proper inclination in respect to the Horizon. 

Note.— Circles of Daily Motion are the circles which the heavenly bodies 
seem to describe as the Earth turns on its axis. 

Examples. 

1. Rectify the Globe for a place whose Latitude is 60 

degrees North. 

2. Rectify the Globe for a place whose Latitude is 30 

degrees South. 

20 



PROBLEMS AND EXAMPLES. 

Problem VIII. 
To find the Antoeci of a given place. 

See note below. 

Find the Latitude of the given place by Problem I. and then 
under the same Meridian find the same degree of Latitude in the 
opposite Hemisphere and it will be the place required. 

Note.— The Antoeci are the inhabitants of the Earth who are located in 
the same Longitude, but in opposite Latitudes; hence in opposite Hemi- 
spheres. 

Examples. 

1. Required the Antoeci of Northern Abyssinia 

2. Required the Antoeci of Barca. 

Problem IX. 
To find the Perioeci of a given place. 

See note below. 

Find the given place and its Latitude and bring the place to 
the Meridian; then turn the Globe on its axis through 180 de- 
grees and under the Meridian in the same Latitude as that of 
the given place, is the place required. 

Note.— The Perioeci are the inhabitants of the Earth who are located in 
the same Latitude, hence in the same Hemisphere but differing in Longi- 
tude 180 degi-ees. 

Examples. 

1. Required the Perioeci of Western California. 

2. Required the Perioeci of Trinidad Island. 

21 



PROBLEMS AND EXAMPLES. 

Problem X. 
To find the Antipodes of a given place. 

See notes below. 

Find the place and its Latitude and bring the place to the 
Meridian; then revolve the Globe through 180 degrees and in 
the opposite Hemisphere under the Meridian and at a distance 
from the Equator equal to the Latitude of the given place is 
the place required. 

Note.— Antipodes are the inhabitants of the Earth who are located at the 
opposite extremities of any one of its diameters. 

Note. — Places situated on the Equator have no Antoeci and their Perkeei 
are their Antipodes. The Poles have no Periceci and their Antoeci are their 
Antipodes. 

Examples. 

1. Required the Antipodes of Sumatra. 

2. Required the Antipodes of Central Greenland. 

Problem XL 
To find places equally distant from a given place. 

See Definition 15. 

Place of the Quadrant on the given place as a center of 
motion and move it around this center on the surface of the 
Globe, and all places over which the same degree of the Quad- 
rant moves are equally distant from the given place. 

Examples. 

1. Find two places equally distant from Cincinnati. 

2. Find three places equally distant from St. Louis. 

22 



PROBLEMS AND EXAMPLES. 

Problem XII. 

The Latitude of a place, its distance and general direction 
from a given place being given, to find the place ivhose Lat- 
itude is given. 

If the distance is given in miles, convert the 
miles into degrees, then place of the Quadrant on the given 
place and move the other end of it Eastward, if the required 
place is Eastward or Westward, if the required place is west- 
ward, till the degree marked on it representing the distance ar- 
rives at the Parallel of Latitude indicating the Latitude of the 
place, and this point will be the place required. 

Examples. 

1. Find the place whose Latitude is 42 degrees North and 

distant from Baltimore in a North-western direction 
9 degrees. 

2. Find the place whose Latitude is 22 g- degrees South and 

distant from Quito in a South-eastern direction 42 
degrees. 

Problem XIII. 

The Longitude of a place, its distance and general direction 
from a given place being given, to find the place whose Long- 
itude is given. 

Reduce the distance, if given in miles, to degrees, 
then place of the Quildrant upon the given place 
and move the other end Northward, if the required place lies 

23 



PROBLEMS AND EXAMPLES. 

Northward, or Southward if the required place lies Southward, 
till the degrees marked on it representing t'he distance arrives at 
the given Meridian and this point will be the place required. 

Examples. 

1. Find the place whose Longitude is 90 degrees West and 

distant in a North-eastern direction from the City of 
Mexico 14 degrees. 

2. Find the place whose Longitude is 20 degrees East and 

distant in a South-western direction from Zanzibar 34 
degrees. 

Problem XIV. 

Any Parallel of Latitude being given, to find how many 
miles make a degree of Longitude on it. 

Place the Quadrant on the given Parallel and note the num- 
ber of degrees intercepted between two Meridians 15 degrees 
apart, then multiply this number by 4 if Geographical miles are 
required, or by 4.6 if Statute miles are required. 

Note.— It will be seen that if the distance between two Meridians 15 de- 
grees apart be measured on the Equator, it will also measure 15 degrees on 
the Quadrant, and this number multiplied by 4 will give 60 the number of 
Geographical miles in a degree, or if multiplied by 4.6 it will give 69, nearly 
the number of Statute miles in a degree. As we go toward the Poles, the 
degrees of Longitude become smaller, and while these same Meridians will 
still be distant from each other 15 degrees of Longitude, the distance 
measured on the Quadrant, which is a uniform standard, will be less than 
15 and this smaller number multiplied by the same multiplier 4 or 4.6, wiU 
give a smaller result. 

24 



problems axd examples. 
Examples. 

1. How many Geographical miles are in one degree on 

the Tropic of Cancer ? 

2. How many Statute miles are in one degree on the Ant- 

arctic Circle? 

Problem XV. 

To find at what rate per Hour any point on the Earth's sur- 
face moves by its axial rotation. 

See Definition 5th. 

If the point is situated on the Equator, reduce 15 degrees 
to miles for the rate per hour, but if it is located between the 
Equator and either Pole, then find by Problem XIV. the num- 
ber of miles that make a degree of Longitude in the Latitide of 
the given place, which number multiplied by 15 will give the 
rate per homr. 

Examples. 

1. ' At what rate per hour do the inhabitants of Rio de 

Janeiro move by the rotation of the Earth on its axis? 

2. At what rate per hour do the inhabitants of Hammerfest 

move by the rotation of the Earth on its axis ? 

Problem XVI. 
To illustrate a Right Sphere. 

See Definition 1, 51. 

Adjust the Globe so that its axis will coincide with the plane 

of the Horizon, then the Equator, Parallels and Circles of 

Daily Motion will be perpendicular to the Horizon. 

25 



problems and examples. 
Examples. 

1. Where would we have to be located on the Earth that 

it might be to us a Right Sphere ? 

2. What is the length of the days and nights at the Equator ? 

3. Could all the Stars in the Heavens be seen from the 

Equator in the course of a year ? 

4. How long would the Sun appear North, and South of the 

Equator during the year ? 

Problem XVII. 
To illustrate a Parallel Sphere. 

See Definition 52. 

To illustrate a Parallel Sphere, adjust the Grlobe so that its 
axis is perpendicular to the plane of the Horizon, then the 
Equator, Paralells and Circles of Daily Motion will be parallel 
to the Horizon. 

Examples. 

1. Where would we have to be located on the Earth that 

it might be to us a Parrallel Sphere ? 

2. How long would there be constant day at each Pole ? 

Problem XVIII. 
To illustrate an Oblique Sphere. 

See Definition 53. 

Adjust the Globe so that its axis will be oblique to the plane 
of the Horizon, then the Equator, Paralells and Circles of Daily 
Motion will also be oblique to the Horizon, 

26 



problems and examples. 
Examples. 

1. Where would we have to be located on the Earth that 

it might be to us an Oblique Sphere ? 

2. Show how the days and nights increase and decrease in 

length on an oblique sphere. 

3. Show why the longest day in the North Temperate Zone 

occurs in June and the shortest day in December. 
Problem XIX. 
To find the Suns place in the Ecliptic on any given day 
of the Year. 

See Definition 23 and note, also Def. 24. 

Find the given day in the Circle of Months on the Horizon 
and opposite this day in the Circle of Signs will be found the 
Sign and degree representing the Sun's Longitude, then find the 
same Sign and Degree in the Ecliptic on the Globe, which will 
show the Sun's place as required. 

Examples. 

1, Find the Sun's place in the Ecliptic on the 1st day of 

May. 

2. Find the Sun's place in the Ecliptic on the 25th of 

October. 

Problem XX. 

See Definition 49 and notes, also Def. 62. 

To find the Sun's Longitude, Right Ascension and Declina- 
tion for any given day in the year. 

Adjust the Globe so that of the Meridian is over the 
Equator, then find the Sun's Longitude by Problem XIX. 

27 



PROBLEMS AND EXAMPLES. 

and turn the Globe on its axis till the Sun's place on the Eclip- 
tic representing the Sun's Longitude arrives at the Meridian. 
Over this degree on the Meridian is the degree showing the 
Sun's Declination, and the distance counted from the First point 
of Aries on the Equator to the Meridan passing through the 
degree found on the Ecliptic, is the Sun's Right Ascension. 

Note — The number of degrees expressing the Sun's Declination subtracted 
from 90 degrees gives the Polar Distance. 

Examples. 

1. Find the Sun's Longitude, Declination and Right As- 

cension on the 20th of August. 

2. Find the Sun's Longitude, Declination and Right As* 

cension on the 1st of December. 

Problem XXL 
To find on what two days of the year the Sun will be ver- 
tical at any given place within the Tropics. 

See Definitions 31, 32. 

Adjust the Globe so that of the Meridian is over the Equa- 
tor, then find the Latitude of the given place on the Meridian 
and revolve the Globe on its axis till two points on the Ecliptic 
pass under the degree of Latitude already found on the Meridi- 
an. Then note the Signs and Degrees on the Ecliptic where 
these points are, and on the Horizon find the Signs and Degrees 
corresponding to them, and exactly opposite the two numbers of 
degrees, in the Circle of Months, are the days required. 

28 



problems and examples. 
Examples. 

1. On which two days of the year will the Sun oe vertical 

20 degrees North of the Equator ? 

2. On which two days of the year will the Sun be vertical 

10 degrees South of the Equator? 

Problem XXII. 

To find the difference of time between any two places 
which are not under the same Meridian. 

Revolve the Globe on its axis till the place that lies East- 
ward of the other place arrives at the Meridian and set the 
Hour Index at XII. Revolve the Globe Eastward till the place 
that lies West comes to the Meridian, then the number on the 
Hour Index under the Meridian will be the number of hours 

required. 

Examples. 

1. Find the difference in time between Greenwich and 

Guayaquil. 

2. Find the difference in time between Columbus and Lake 

Tchad. 

Problem XXIII. 

The hour being given at any place, to determine what 
hour it is at any other given place. 

Find the difference of time between the two places by Prob- 
lem XXII. then if the place whose time is required is East of 
the place whose time is given, add this difference to the given 
time, but if the place whose time is required is "West, subtract 

29 



PROBLEMS AND EXAMPLES. 

this difference from the given time, and the result will be the 
time required. 

Examples. 

1. If it is 10 o'clock A. M. at Madrid what time is it at 

Rome? 

2. If it is 4 o'clock P. M. at Charleston what time is it at 

Richmond ? 

Problem XXIV. 

lo find the time of the $uris rising and setting on any 
given day at a "place ivhose Latitude is given. 

Find the Declination of the Sun by Problem XX. and elevate 
the pole corresponding to the Sun's Declination as many degrees 
as that of his Declination, and bring the given place to the Me- 
ridian and set the Hour Index at XII. Then turn the Globe 
Westward on its axis till the given place comes to the Horizon, 
and the Hour Index will indicate the time of the Sun's rising, 
and by turning the Globe Eastward on its axis till the given 
place comes to the Horizon, the Hour Index will show the time 
of the Sun's setting. 

Examples. 

1. At what time does the Sun rise and set at Toronto on 

the 1st of March ? 

2. At what time does the Sun rise and set at Melbourne on 

the 1st of November ? 
30 



PROBLEMS AND EXAMPLES. 

Problem XXY. 

lo find all places where the Sun is vertical on a given day. 

Find the Sun's Declination for the given day according to 
Problem XX. and revolve the Globe once on its axis, and all 
places on the Globe that have the Sun vertical on that day will 
pass under the degree on the Meridian that indicates the Sun's 
Declination for the given day. 

Examples. 

1. At what places is the Sun vertical on the 1st of July? 

2. At what places is the Sun vertical on the 1st of Jan- 

uary ? 

Problem XXVI. 
The day and hour of the day at any place being given, 
to find where the Sun is vertical at that time. 

See Definition 49 and notes, also Def. 80. 

Find the Sun's Declination by Problem XX. and elevate the 
Pole corresponding to the Declination as many degrees as that 
of the Declination and bring the place on the Globe whose time 
is given to the Meridian and set the Hour Index at XII. Then 
revolve the Globe Westward, if the given time is before noon, 
or Eastward if the given time is past noon, through as many 
hours and minutes as it is before or past noon, and the point 
under of the Meridian will be the required place. 

Examples. 
1. Where is the Sun vertical at 9 o'clock, A. M. on the 

1st of June ? 

31 



PROBLEMS AND EXAMPLES. 

2. Where is the Sun vertical at 4 o'clock, P. M. on the 
1st of September? 

Problem XXVII. 

To find the Month and Day of the month when the Sun's 
place in the Ecliptic is in any given Degree, in any given 
Sign. 

Find on the Globe the Sign and Degree which show the 
Sun's place ; then find the same Sign and Degree as marked 
on the Horizon and opposite this degree in the Circle of Months 
is the day required. 

Examples. 

1. Find the Month and Day of the month when the Sun 

will be in the 30th degree o? Taurus. 

2. Find the Month and Day oP the month when the Sun 

will be in the 20th degree of Scorpio. 

Problem XXVIII. 
To find on a given day those portions of the Earth on 
which the Sun does not Rise or Set. 

Find the Declination of the Sun by Problem XX. for the 
given day; then elevate the Pole corresponding with his Decli- 
nation an equal number of degrees above the Horizon with that 
of his Declination. Revolve the Globe once Eastward on its 
axis and to all that portion of the Globe around the elevated 
Pole that does not descend below the Horizon the Sun does 
not set, and to all that portion of the Globe around the depress- 

32 



PROBLEMS AND EXAMPLES. 

ed Pole that does not ascend above the Horizon the Sun does 
not rise. 

Examples, 
i 1. Find the regions of the Earth where the Sun neither 
rises nor sets on the 21st of December. 
2. Find the regions of the Earth where the Sun neither 
rises nor sets on the 21st of June. 

Problem XXIX. 

At any given place and on any given day of the Year, to 
find the length of the Day, and also of the Night. 

Find the time of the Sun's rising and setting for the Lati- 
tude of the given place on the given day by Problem XXIV*. 
then the length of the Day is found by doubling the time of 
the Sun's Setting, and the length of the Night is found by 
doubling the time of the Sun's rising. 

Examples. 
1. How many Hours Long is the Day, also the Night at 

Paris on the 20th of August ? 
1. How many Hours Long is the Day, also the Night" at 

Montreal on the 20th of February ? 

Problem XXX. 

At any Given Place on any day of the Year, to find the 
Sun's Meridian Altitude and Zenith Distance. 

See Definitions 55, 56, 57, 58, 59. 

Elevate the Pole corresponding to the Latitude of the given 
33 



PROBLEMS AND EXAMPLES. 

place as many degrees as that of the Latitude of the place, and 
find the Sun's place in the Ecliptic for the given day by Prob- 
lem XTX. then bring the Sun's place to the Meridian and the 
number of degrees counted on the Meridian to the Horizon 
from the Sun's place is the required Altitude, and the difference 
between this number and 90 degrees is the Zenith Distance. 

Examples. 

1 . Find the Sun's Meridian Altitude and Zenith Distance 

at Havannah on the 1st of November. 

2. Find the Sun's Meridian Altitude and Zenith Distance. 

at Cincinnati on the 20th of April. 

Problem XXXI. 

To find the Sun's Altitude and Zenith Distance at any 
given hour of any given day at any given place. 

Elevate the Pole corresponding to the Latitude of the given 
place as many degrees as that of the Latitude of the place, and 
find the Sun's place in the Ecliptic for the given day by Prob- 
lem XIX. then bring the Sun's place to the Meridian and set 
the Hour Index at XII. Revolve the Grlobe Westward if 
the given time be before noon, cr Eastward if the given time be 
after noon, through as many hours as the given time is before 
or after noon. This being done attach the Quadrant to the Ze- 
nith point of the Meridian and move the other end over the 
Globe till its graduated edge comes to the Sun's place, and the 
number of degrees counted on the Quadrant from the Hoiizon 
tojbhe Sun's place will be the required Altitude, and the num- 

34 



PROBLEMS AND EXAMPLES. 

ber counted from the Sun's place to the Zenith will be the Ze- 
nith distance. 

Examples. 

1. What is the Suns Altitude and Zenith Distance at 

Berlin on the 10th of May at 2 o'clock P. M ? 

2. What is the Suns Altitude and Zenith Distance at Bue- 

nos Ayres on the 20th of December at 11 o'clock A. M? 

Problem XXXII. 

To find the Hour of any given day at any given place 
when the Sun's Altitude is given. 

Rectify the Globe for the Latitude of the place and find the 
Sun's Place in the Ecliptic by Problem X IX, then bring his 
place to the Meridian and set the Hour Index at XII. This be- 
ing done attach the Quadrant to the Zenith point and move the 
other end over the Globe and a^ the same time revolve the 
Globe on its axis till the Sun's place and the degree on the 
Quadrant expressing the Sun's Altitude coincide, and the Hour 
Index will show the number of hours required before or after 
noon. 

Examples. 

1. When the Sun's Altitude at Aspinwall on the 15th of 

July is 30 degrees, what is the Hour of the Day ? 

2. When the Sun's Altitude at Sidney on the 1 tJth of 

December is 50 degrees, what is the Hour of the Day? 

35 



PROBLEMS AND EXAMPLES. 

Problem XXXIII. 

To find the Bearing and distance of one place from another. 

See Definitions 60, 71, 72, 73. 

Elevate the pole that corresponds to the Latitude of one of 
the places to the Latitude of that place, and bring the place to 
the Meridian; then attach {he Quadrant to the Meridian imme- 
diately over the place and carry the other end around on the 
surface of the Globe till its graduated edge touches the other 
place, and the Azimuth will give the bearing of the second place 
from the first, and tke number of degrees counted on the Quad-, 
rant between the two Places multiplied by the number of miles 
in a degree will give 'the distance between the two places in 
miles. 

Examples. 

1. Find the Bearing and Distance of London from New 

York. 

2. Find the Bearing and Distance of Cape Horn from the 

Cape of Good Hope. 

Problem XXXIV. 

To find that part of the Globe where the Sun ceases to 
rise and that part where he ceases to set on any given day. 

Find the Sun's Declination by Problem XX. for the given 
day and elevate the corresponding Pole above the Horizon as 
many degrees as expresses his Declination; then revolve the 
Globe on its axis and the boundary of that portion of the Globe 
that does not descend below the Horizon shows the places where 

3fi 



PROBLEMS AND EXAMPLES. 

the Sun has ceased to set, and the boundry of that portion of 
the G-lobe that does not rise above the Horizon shows the 
places where the Sun has ceased to rise. 

Examples. 

1. On what Parallel does the Sun cease to rise and also 

cease to set on the 25th of May ? 

2. On what Parallel does the Sun cease to rise and also 

cease to set on the 12th of November? 

Problem XXXV. 

To find when Twilight Begins, Ends and its Duration on 
any given day at any given place in the Torrid or Temperate 

Zones. 

See Definitions 35, 36, 37, 43. 

Find the Declination of the Sun for the given day by Prob- 
lem XX. and elevate the Pole corresponding to the Declination 
of the Sun as many degrees as that of his Declination on the 
given day, and bring the given place to the Meridian and set 
the Hour Index at XII. Then revolve the Globe Eastward til[ 
the given place comes to the Horizon and the Hour Index will 
show the time at which the Sun sets and Twilight begins. 
Now attach the Quadrant to the Meridian at and bring its 
graduated edge to the given place and continue to revolve the 
Grlobe till the Quadrant shows the given place to be 18 degrees 
below the Horizon, and the Hour Index will indicate when the 
evening twilight ends, and the difference between the hours of 
its beginning and ending will be its duration. 

37 

* 



problems and examples. 
Examples. 

1. At what Hour does the Sun set, and at what Hour 

does Twilight end at Vienna on the 6th of December? 

2. At what Hour does the Sun set, and at what Hour 

does Twilight end at the Island of St. Helena ? 

Problem XXXVI. 

To find the Sun's Azimuth and Amplitude at any given 
place for any given hour on any given day. 

See Definition 61 and notes, also Def. 26 and notes. 

Elevate the pole corresponding to the Latitude of the place 
as many degrees as that of the Latitude and attach the Quad- 
rant to the Meridian at 0. Next find the Sun's 6 place in the 
Ecliptic by Example XIX. and bring it to the Meridian and 
set the Hour Index at XII. Then if the time be before noon 
turn the Globe Eastward, or if it be afternoon, turn it Westward 
through as many hours as the time is before or after noon, and 
pass the Quadrant through the Sun's place on the Ecliptic, and 
the number of degrees counted on the Horizon from the North 
Point or from the South Point, if it be the nearer of the two, to 
the Quadrant will be the Azimuth, and the number counted 
from the East or from the West point, if it be the nearer will 
be the Amplitude. 

Note. — It Avill be observed that the Azimuth and Amplitude are comple- 
ments of each other, and if either be known the other may be found by sub- 
racting the known number from 90 degrees. 

38 



problems and examples. 
Examples. 

1. What is the Sun's Azimuth and Amplitude at Glasgow 

at 8 o'clock A. M. on the 10th of January? 

2. What is the Sun's Azimuth and Amplitude at Valpariso 

at 3 o'clock P. M. on the 10th of June? 

Problem XXXYII. 

The Sun's Amplitude or Azimuth being given at any given 
hour of any given day to find the Latitude of the place of 
the observer. 

Find the Sun's place on the Ecliptic for the given day by 
Problem XIX. and bring his place to the Meridian and set the 
Hour Index at XII. Then if the given time be before noon re- 
volve the Globe Eastward, or if it be after noon revolve the Globe 
Westward, through as many hours as the given time is before or 
after noon. This being done attach the Quadrant to the Meridian 
at and move the other end till it arrives at the given degree 
of Azimuth or Amplitude on the Horizon and retain it in this 
position; then without allowing the Globe to turn on its axis 
elevate or depress whichever pole requires it, till the Sun's place 
arrives at the Quadrant, and the elevation of the pole above the 
Horizon will sho,w the Latitude of the place of the observer. 

Examples. 
1. If the Sun's Amplitude is 30 degrees North of the 
East point at 9 o'clock A. M. on the 5th of February, 
what is the Latitude of the Observer ? 

39 



PROBLEMS AND EXAMPLES. 

2. If the Sun's Azimuth is 45 degrees West of South at 
4 o'clock P. M. on the 30th of July, what is the Lati- 
tude of the Observer ? 

Problem XXXVIII. 

To find at what time the Sun will he due East or due 
West from any given place on any given day. 

Rectify the Globe for the Latitude of the given place and 
find the Sun's place in the Ecliptic by Problem XIX. for the 
given day, and bring it to the Meridian and set the Hour Index 
at XII. Attach the Quadrant to the Meridian at and move 
its other end on the surface of the Globe till its graduated edge 
arrives at the East point of the Horizon. Then revolve the 
Globe on its axis till the Sun's place arrives at the edge of the 
Quadrant, and the Hour Index will show the number of hours 
before noon when the Sun will be due East and at the same 
time past noon he will be due West. 

Examples. 

1. At what hour will the Sun be due East from Pitts- 

burg on the 1st of April. 

2. At what hour will the Sun be due West from 

Queen Charlotte Islands on the 5th of August ? 

Problem XXXIX. 
To find that Part of the Equation of Time or difference 
between Clock and Sun Time, which depends on the Obliqui- 
ty of the Ecliptic, for any given day. 

See Definition 23 and note, also Def. 24. 
40 



PROBLEMS AND EXAMPLES. 

Find the Sun's place in the Ecliptic for the given day by 
Problem XIX. and bring it to the Meridian; then find the num- 
ber of degrees to the Meridian in the order of the Signs from 
the First point of the Sign Aries reckoned on the Equator and 
also on the Ecliptic, and subtract the less from the greater. 
Reduce this difference to minutes by multiplying by 4, as there 
are 4 minutes of time in a degree, and it will give the 
Equation of time. 

Note. — If the number of degrees on the Ecliptic exceed those on the Equa- 
tor the Sun time is faster than clock time, but if the number of degrees on 
the Equator exoeed those on the Ecliptic, Sun Time is slower than Clock 
Time. 

Examples. 

1. What is the Equation of time on the 3d of November? 

2. What is the Equation of time on the 15th of May ? 

Problem XL. 
At any given 'place in the North Frigid Zone, to find the 
beginning and end of constant day. 

See Definitions 34, 38, 39. 

Adjust the Globe so that the Equator is under of the Me- 
ridian and bring the First point of Aries to the Meridian; then 
find the number of degrees expressing the Latitude of the place 
and subtract this number from 90 degrees and count on the 
Meridian Southward from the Equator the number of degrees 
expressing this difference, and note this number. Next revolve 
the Globe Westward on its axis, and observe in what Signs and 
at what Degrees the two points of the Ecliptic are that pass 

41 



PROBLEMS AND EXAMPLES. 

under this number, and on the Horizon opposite the same 
Signs and Degrees taken in ths same order are found the two 
days which are respectively the beginning and the end of con- 
stant day. 

Note. — The same Solution may be used for any point in the South Frigid 
Zone by observing to reckon the difference of degrees Northward instead 
of Southward from the Equator. 

Examples. 

1, Find the Beginning, and End of constant day at Ham- 

merfest. 

2. Find the Beginning, and End of constant day 15 de- 

grees South of the Antarctic Circle. 

. Problem XLI. 

The Month, Day and Hour of the day being given at 
any place, to find where the Sun is vertical, and all places 
that have noon, and all places that have midnight. 

Find the Sun's Declination by Problem XX. and elevate the 
pole corresponding to his Declination as many degrees as that 
of his Declination and bring the given place to the Meridian 
and set the Hour Index at XII. Then if the given time be 
before noon revolve the Globe Westward through as many 
hours as it is till noon ; but if the given time be after noon 
revolve the Globe Eastward through as many hours as it is 
past noon, and all places under the Meridian above the Hori- 
zon will have noon, and all places under the Meridian below 

42 



PROBLEMS AND EXAMPLES. 

the Horizon will have midnight, and the point under of the 
Meridian will be the place where the Sun is vertical. 

Examples. 

1. When it is Noon at Philadelphia on the 10th of April, 

at what particular j»lacj is the S m vertical, what 
other places have noon, and what places have mid- 
night ? 

2. When it is Midnight at Montevideo on the 10th of 

November, at what particular place is the Sun verti- 
cal, what other places have midnight, and what places 
have noon. 

Problem XLII. 

lo find the Suns Longitude and Declination by the Ana- 
lemma for any given day. 

See Analemma on the Globe. 

Adjust the Grlobe so that the Equator is under of the Me- 
ridian. Then find the given day on the Analemma and 
revolve the Globe till it arrives at the Meridian, and the degree 
on the Meridian over the given day will be the Sun's Decli- 
nation. 

To obtain the Sun's Longitude, find the point of the Eclip- 
tic on the Globe which corresponds with the given day by 
Problem XIX. and the number of degrees counted on the 
Ecliptic Eastward from the First Point of the Sign Aries to 
the Sun's place, will be his Longitude. 

43 



problems and examples. 
Examples. 

1. Find by the Analemma the Sun's Declination and 

Longitude on the 1st of June. 

2. Find by the Analemma the Sun s Declination and 

Longitude on the 24th of November. 

Problem XLIII. 

To find by the Analemma on what two Days of the Year 
the Sun will be vertical at any given place within the Tropics. 

Adjust the Globe so that of the Meridian is over the 
Equator. Then find the Latitude of the given place on the 
Meridian and revolve the Globe on its axis till the Analemma 
arrives at the Meridian. Under the degree on the Meridian, 
showing the Latitude of the place, are found the required 
days. 

Examples. 

1. Find by the Analemma on what two Days of the Year 

the Sun will be vertical 15 degrees South of the Equa- 
tor. 

2. Find by the Analemma on what two days of the Year 

the Sun will be vertical 10 degrees North of the 
Equator. 

Problem XLIV. 
To find by the Analemma all places where the Sun will 
he vertical on a given day. 

Adjust the Globe so as to bring the Equator under of the 
44 



PROBLEMS AND EXAMPLES. 

Meridian. Then find the given day on the Analemma and re- 
volve the Globe till the Analemma arrives at the Meridian, and 
the degree on the Meridian over this day will show the Sun's 
Declination ; and if the Globe, is made to turn once Eastward 
on its axis all places which pass under this degree of the Meri- 
dian will have a vertical Sun. 

Examples. 

1. Find by the Analemma all places where the Sun is 

vertical on the 1st of April. 

2. Find by the Analemma all places where the Sun is 

vertical on the 1st of November. 

Problem XLV. 

At any given plakic in the North Frigid Zone, to jind by 
the Analemma the length of the longest day. 

Adjust the Globe so that the Equator will be under of the 
Meridian. Then find the Latitude of the given place in degrees 
and the Complement of the Latitude, which is the difference 
between its Latitude and 90 degrees. Count Northward from 
the Equator on the Meridian as many degrees as that of the 
Complement, and note the last degree. Then revolve the Globe 
on its axis till the Analemma arrives at the Meridian and the 
two days under this degree will show the beginning and end of 
the longest day. 

Examples. 

1. Find by the Analemma the length of the longest day 

10 degrees North of the Arctic Circle. 
45 



PROBLEMS AND EXAMPLES. 

2. Find by the Analemnia the length of the longest day 
20 degrees North of the Arctic Circle. 

Problem XLYI. 

Any place being given in the South Frigid Zone, to find 
by the Analemma the length of the longest day. 

Adjust the Globe so that the Equator will be under of the 
Meridian, and find the Latitude of ih.3 given place in degrees 
and its Coniplern.nt. Then count Southward^ from the Equa- 
tor on the Meridian the number of degrees equal to the Com- 
plement and note the degree where this number ends. Re- 
volve the Globe on its axis till the Analenmiu comes under the 
Meridian and the two days under the degree noted will show 
the beginning and end of the longest day. 

Examples. 

1. Find by the xxnalemnia the length of the longest day 

5 degrees South of the Antarctic Circle. 

2. Find by the Analemma the length of the longest day 

15 degrees South of the Antarctic Circle. 

Problem XL VII. 

Any place being given in either of the Frigid Zones, to find 
by the Analemma: the length of the longest night. 

Adjust the Globe so that the Equator will be under of the 
Meridian and subtract the number of degrees expressing the 
Latitude of the given place from 90, and count from the Equa- 
tor Southward if the place be in the North Frigid Zone, or 

46 



PROBLEMS AND EXAMPLES. 

Northward if the place be in the South Frigid Zone, the num- 
ber of degrees expressing this difference, and note this number. 
Then revolve the Globe on its axis till the Analemma comes 
under the Meridian and the two days under the degree noted 
will show the beginning and end of the longest night, 

Examples. 

1. Find by the Analemma the length of the longest night 

at Spitsbergen Island. 

2. Find by the Analemma the length of the longest night 

at Mt, Erebus. 

Problem XLVIII. 

The longest and the shortest days in either Hemisphere 
being given, to find the width of the Torrid Zone. 

Adjust the Globe so that of the Meridian is over the 
Equator and find by the Analemma the Sun's Declination ibr 
the two given days, and the sum of these Declinations will be 
the width of the Torrid Zone in degrees, and its width in Geo- 
graphical or Statute miles may be found by multiplying by CO 
or 69.1. 

Examples. 

1. If the longest day in the Northern Hemisphere is the 

21st of June and the shortest day the 22nd of 
December, what is the width of the Torrid Zone ? 

2. If the width of the Ton-id Zone is 47 degrees, what is 

the width of each of the other Zones ? 

47 



PRO*>\EMS AND EXAMPLES. 

Problem XLIX. 

The time of the Occurrence of a Lunar Eclipse, in the 
mean Solar time of any place being given, and its duration,, to 
find those parts of the Earth where the beginning and the 
end of the Eclipse are visible, and also those regions where 
the Eclipse is visible throughout its duration. 

Find the Declination of the Sun by Problem XX. and ele- 
vate the pole corresponding to his Declination as many degrees 
above the Horizon as the Declination. Then bring the place 
from which the time is reckoned to the Meridian and set the 
Hour Index at XII. Turn the Globe Westward or Eastward 
according as the time is before or after noon through as many 
hours as the beginning of the Eclipse is before or after noon, 
iinl to all that Hemisphere below the Horizon the beginning 
of the Eclipse will be visible. Next turn the Globe Eastward 
through as many hours as are equal to the duration of the 
Eejipse and to all that Hemisphere now below the Horizon the 
end of the Eclipse will be visible, and to all those regions com- 
mon to these two Hemispheres below the Horizon the Eclipse 
will be visible throrghout its duration. 

Examples. 

1. If a partial Eclipse of the Moon begins at 7 o'clock 

P. M., Pittsburgh Time, on the 10th of November 

and lasts one hour, in what regions is it visible 
throughout its duration ? 

48 



PROBLEMS AND EXAMPLES. 

2. If an Eclipse of the Moon begins at 2 o'clock A. M. 
Washington time, on the 15th of July and lasts two 
hours, in what regions is it visible throughout its 
duration ? 

Problem L. 

The time of the occurrence of a Solar Eclipse in the 
mean Solar time of any 'place being given, and its dura- 
tion, to find those regions on the Earth in which it is visible. 

iVdjust the Globe so as to bring the Equator under of the 
Meridian. Then find the declination of the Sun for the given 
day and note it. Next bring the place from which the time is 
reckoned to the Meridian and set the Hour Index at XII. 
Then turn the Globe on its axis Westward if the given time be 
before noon or Eastward if it be after noon, through as many 
hours as the beginning of the Eclipse is before or after noon. 
To that point on the Earth which is now under the degree on 
the Meridian corresponding to the declination of the Sun, the 
Sun will be vertical, and to all places within 35 degrees of 
this point the beginning of the Eclipse will be visible. Then 
turn the Globe Eastward on its axis through as ^nany hours as 
are equal to the duration of the Eclipse and note where the 
Sun is vertical, and to all places within 35 degrees of this 
point the end of the Eclipse will be visible, and to all regions 
which are common to the two Areas thus found the Eclipse 
will be visible throughout its duration. 



49 



problems and examples. 
Examples. 

1. If an Eclipse of the Sun begins at 10 o'clock A. M., 

New York time, on the 25th of August, and con- 
tinues 30 minutes, in what regions is it visible 
throughout its duration ? 

2. If an Eclipse of the Sun begins at 3 o'clock P. M., 

Chicago time, on the 31st of October, and continues 
50 minutes, in what regions is it visible throughout 

its duration ? 



50 



DEFINITIONS AND EXPLANATIONS. 



The Earth on which we dwell is the third primary- 
planet of the eight that revolve around the Sun. Her 
mean distance from the Sun is about 91,430,000 miles and 
she revolves once around him in about 365^ days, and 
rotates once on her axis in about 24 hours. The distance 
through her center from North to South, which is her Po- 
lar diameter, is about 7,899 miles, and the mean distance 
from any point of her Equator to the opposite point, 
which is her Equatorial diameter, is about 7,926 miles. 
In consequence of the difference of about 26J miles in 
the lengths of these diameters, she is not a sphere, but an 
Oblate Spheroid, which means a sphere flattened on the 
opposite sides. * 

1. A Sphere is a solid or volume bounded by a sur- 
face, every point of which is equally distant from a point 
within, called the center. 

2. The Radius of a Sphere is a straight line drawn 
from the center to any point in the surface. 

3. The Diameter of a Sphere is a straight line 

drawn through its center and each end terminating in its 

surface. 

* Note. — The earth's equatorial circumference is an ellipse whose 
major axis is 1% miles longer than its minor axis. 



DEFINITIONS. 

4. The axis of the earth is the diameter on which 
it turns once in about 24 hours, and the same imaginary 
line continued North and South until it meets the starry 
heavens constitutes the axis of the Celestial Sphere. 

5. The poles of the earth are the extremities of 
the Earth's axis, and the poles of the heavens are the 
extremities of the Celestial axis. 

6. A circle is a plane surface bounded by a curved 
line, every point of which is equally distant from a point 
within, called the center. ^ 

7. The circumference of a circle is the line that 
bounds the circle. 

8. The radius of a circle is any straight line drawn 
from its center to its circumference. 

9. The diameter of a circle is any straight line 
passing through its center and each end terminating in its 
circumference. 

10. An arc is any part of a circumference. 

it. A plane is a surface such that if any two points be 
taken in it, a straight line joining these points will be 
wholly in the surface. 

12. A curved surface is a surface which is neither 

a plane nor composed of planes. 

* Note. — The word circle, is used instead of circumference in de 
scribing lines on the surface of the globe. 

Note. — The phrase, plane of the circle, is used to denote the 
circle proper. 



DEFINITIONS. 

13. A straight line is one that does not change its 
direction at any point. 

14. A curved line is one that changes its direction at 
every point. 

15. A Point is that which has position, but not mag- 
nitude. 

16. Parallel lines are such as have the same di- 
rection, and are therefore equally distant from each 
other at all corresponding points. 

17. An angle is the opening or difference in direc- 
tion between two lines which meet in a common point 
called the vertex. 

18. A right angle is one that is equal to 90 degrees 
and is the angle which may be formed by drawing a ver- 
tical and a horizontal radius in a circle. 

19. An Acute Angle is one that is less than a 
Right angle, 

20. An obtuse angle is one that is greater than a 
Right angle. * 

21. A great circle is one which passes through the 
center of a Sphere and divides it into two equal parts, f 

* Note. — Oblique Angles, embrace the two proceding classes, 
Obtuse and Acute. 

•j- Note. — For the sake of convenience, both the Earth and the 
Heavens are conceived to be marked by Points and divided into parts 
by Lines and Circles, whose Planes cut through them in various di- 
rections. 

Note. — Every Circle, great or small is conceived to be divided 
into 360 equal parts called degrees, therefore a degree is not a fixed 
quantity, but only an aliquot part of any Citcle. 



DEFINITIONS. 

22. The equator is a great Circle which cuts the 

Earth at Right angles with its Axis, and divides it into 

the Northern and Southern Hemispheres. 

Note. — The intersection of the plane of the Equator with the 
surface of the Earth, constitutes the Terrestrial Equator, and with the 
concave Sphere of the Heavens the Celestial Equator or the Equi- 
noctial. 

23. The ecliptic, is a great Circle in which the 
Earth performs her annual revolution around the Sun, 
and also in which is the apparent path of the Sun. 

Note. — The Orbit of the Earth, is her pathway in the Ecliptic. 

24. The obliquity of the ecliptic is the inclina- 
tion of the Ecliptic to the Equinoctial of about 23J de- 
grees. 

25. The equinoctial points are the intersections of 
the Ecliptic and Eqninoctial. 

Note. — In consequence mainly of the Solar and Lunar attraction 
xipon the excess of matter around the Equator of the Earth, it is slight- 
ly disturbed in its yearly motion, causing the intersections of the Eclip- 
tic with the Equinoctial to move westward about 50" annually. 

26. Meridians are great Circles, which pass through 

the North and South points, and cross the Equator at 

Right angles. 

Note. — The First or Prime Meridian, is the Meridian from 
which Longitude is reckoned East or West. Longitude is sometimes 
reckoned from the Meridians of Ferro, Paris, Madrid and Washington, 
but usually from the Meridian of Greenwich, England. 

Note. — The word Meridian frequently denotes the upper half of 
-a great Circle, which passes through the North and South points. 

Note. — Meridians are sometimes called Hour Circles, and also 
lines of Longitude, because the Arcs of the Equator intercepted be- 
tween them, are used as measures of Time and Longitude. 



DEFINITIONS. 

27. The Equinoctial Colure is the Meridian which 
passes through the Equinoctial points. 

28 The Solstitial Colure is the Meridian which pass- 
es through the Solstitial points. 

The Solstitial Points are the points where the 

Ecliptic touches the Northern and Southern Tropics. 

Noe. — The East and West points are equidistant from the Poles 
of the Earth, and are where the Sun rises and sets when the Days and 
Nights are equal. 

29. A Small Circle is one that divides a Sphere into 
two unequal parts, as it does not pass through the centre 
of the Sphere. 

30. Parallels of Latitude are small Circles, paral- 
lel to the Equator, and when extented into the Heavens, 
are called Parallels of Declination. 

31. The Tropic of Cancer is the Parallel of Lati- 
tude which touches the Northern point of the Ecliptic 
called the Summer Solstice. 

32. The Tropic of Capricorn is the Parallel of Lati- 
tude which touches the Southern point of the Ecliptic 
called the Winter Solstice. 

32. The Arctic or North Polar Circle is the 
Parallel of Latitude which passes through the Pole of the 
Ecliptic, distant about 2^/2 degrees from the North Pole. 

34. The Antarctic or South Polar Circle is the 
parallel of latitude which passes through the Pole of the 
Ecliptic, distant about 23^ degrees from the South Pole. 



DEFINITIONS. 

35. Torrid Zone, is that portion of the Earth's 
surface which lies between the Tropics. 

36. The North Temperate Zone is that portion of 
the Earth's surface which lies between the Tropic of 
Cancer and the Arctic Circle. 

37. The South Temperate Zone is that portion of 
the Earth's surface which lies between the Tropic of Cap- 
ricorn and the Antarctic Circle. 

38. The North Frigid Zone is that portion of the 
Earth's surface which lies North of the Arctic Circle. 

39. The South Frigid Zone is that portion of the 
Earth' surface which lies South of the Antarctic Circle. 

40. The Sensible Horizon is a Circle touching the 
Earth at the spectators feet and extending to the Heavens. 

41. The Visible Horizon is the line where the Sky 
and Earth seem to meet, forming a Circle around the 
spectator. 

42. The Rational Horizon is a Great circle which 

is parallel to the Sensible Horizon and distant from it 

nearly 4.000 miles, the semi-diameter of the Earth, and 

divides the Earth into upper and lower Hemispheres and 

separates the visible Heavens from the invisible. 

Note. — In consequence of the vast distance to the Starry Sphere ; 
these Horizons seem to coincide in it, so that we see the same Hem- 
isphere of stars that we would see if the upper half of the Earth were 
removed and we were standing on the Rational Horizon. 

Note, — Every place on the Earth has its own Horizon. 



DEFINITIONS. 

43. Refraction of Liokt is the deflection of the rays 
from their original course,Jjy the medium through which 
they pass. 

44. The Cardinal Points when referred to the Earth 
are North, South, East and West, when referred to the 
Heavens are the Zenith and Nadir, ancf when referred to 
Ecliptic, they are the Equinoxes and Solstices. 

45. The Mariners Compass is composed of a Mag- 
netic Needle, free to move on a sharp-pointed support 
erected in the centre of a Dial which is divided into 
thirty two equal parts representing the Cardinal and In- 
termediate points of the Horizon. 

46. The Latitude of a place on the Earth is its 
distance measured on its Meridian North cr South from 
the Equator. 

47. The Polar distance of a place on the Earth 
is its distance measured on its Meridian from the nearest 
Pole. 

Note. — Latitude and Polar distance are mutually comple- 
ments of each other, as each is measured on the same Meridian, in op- 
posite directions, just 90 degrees. 

48. Longitude is distance measured on the Equator 
or a Parallel from some Standard Meridian, called the 
First or Prime Meridian, East or West, from o to 180 de- 
grees. 



DEFINITIONS. 

49. Right Ascension is distance Eastward from the 
First Point of the Sign Aries, measured on the Equi- 
noctial from o to 360 degrees. 

Note. — The Declination of a heavenly body, is its distance North 
or South from the Equinoctial. 

Note. — Declination corresponds to Terrestrial Latitude. 

Note. — The Polar distance of a Star, is the complement of its 
Declination. 

50. The Zodiac is that part of the Celestial Sphere 
which lies about 8 degrees on each side of the Ecliptic. 

51. A Right Sphere is one whose Axis lies wholly in 
the Plane of the Horizon, hence the Equator, Parallels 
and Circles of daily motion, are perpendicular to the 
Horizon. 

52. A Parallel Sphere is one whose Axis is perpen- 
dicular to the Plane of the Horizon, hence the Equator 
coincides with the Horizon, and the Parallels and Circles 
of a daily motion, are Parallel with the Horizon. 

53. An Oblique Sphere is one whose Axis is oblique 

to the Horizon, hence the Equator, Parallels and Circles 

of daily motion, are oblique to the Horizon. 

Note. — The definitions of the different Points, Lines and Circles 
which are used in Astronomy, and the propositions based upon them, 
compose the Doctrine of the Sphere. 

54. The Poles qf the Horizon are the Zenith and 
Nadir. 

55. The Zenith is that point in the Celestial Sphere, 
directly over the observers head. 

56. The Nadir is that point in the Celestial Sphere, 
directly under our feet. 



DEFINITIONS. 

57. A vertical circle is one that passes through the 
Zenith and Nadir and is perpendicular to the plane of 
the Horizon. 

58. The altitude of a heavenly body is its eleva- 
tion above the Horizon, measured on a vertical circle. 

59. The zenith distance of a heavenly body is the 
complement of its altitude, that is the difference between 
the altitude and 90 degrees. 

60. The azimuth of a heavenly body is the angular 

distance between the plane of the Meridian and that of a 

vertical circle passing through the body, and both passing 

through the Zenith. 

Note. — Azimuth is reckoned on the Horizon East or West from the 
North and South points, from o to 90 degrees. 

61 . The amplitude of a heavenly body is the angular 
distance from the Prime Vertical to a vertical circle pass- 
ing through the body. 

Note. — Amplitude is reckoned on the Horizon North or South from 
the Prime Vertical, from o to 90 degrees. 

Note. — Azimuth and Amplitude are mutually complements of each 
other, as each is measured on the same great circle in opposite directions 
just 90 degrees. 

62. Celestial longitude is angular distance East 
from the first point of the Sign Aries, measured on the 
Ecliptic from o to 360 degrees. 

63. Celestial Latitude is angular distance meas- 
ured on a Secondary from the Ecliptic, from o to 90 
degrees. 



DEFINITIONS. 

64. — The axis of a GREax circle is a straight line pass- 
ing through its center at Right Angles to its Plane. 

65. The pole of a great circle is the Point where its 
Axis cuts through the surface of the Sphere. 

66. Every great circle has two Poles, each of which 
is 90 degrees from the Great Circle. 

Note. — A great circle which passes through the Pole of another 
Great Circle, cuts the latter at Right Angles and is called a Secondary 
to that Circle. 

Note. — Meridians are Secondaries to the Equator. 

67. Perihelion is that point in the Earth's Orbit 
nearest the Sun. 

68. Aphelion is that point in the Earth's Orbit farth- 
est from the Sun. 

69. The line of the apsides is the line joining the 
Perihelion and Aphelion points. 

70. Angular distance is the difference in direction 
between two points as seen from a third point. 

71. Angular motion is the motion of a point or body 
around another point which is at rest. 

72. Angular velocity is the rate of angular motion. 

Note. — We ascertain the position of a given place on the Globe or 
in the Heavens, by taking its angular distance from two Great Circles, 
the Horizon and the Meridian, or the Horizon and the Prime Vertical, 
they being Coordinate Circles are used for such measurements. 

73. The autumnal equinox is the time when the Sun 
crosses the Equator in going Southward, which occurs 
about the 2 2d of September. 



- DEFINITIONS. 

74. The vernal equinox is the time when the Sun 
crosses the Equator in returning Northward, which occurs 
about the 21st of March. 

75. The solstitial points are the two points of the 
Ecliptic most distant from the Equinoctial. 

76. The summer solstice is the time when the Sun 
is at his greatest distance North of the Equinoctial, which 
occurs about the 21st of June. 

77. The winter solstice is the time when the Sun is 
at his greatest distance South of the Equinoctial, which 
occurs about the 22d of December. 

78. The circle of perpetual apparition is the 
boundary of that spice in the Heavens around the eleva- 
ted Pole in which the Stars never set. 

79. The circle of perpetual occult ation is the 
boundary of that space in the Heavens around the de- 
pressed Pole in which the Stars never rise. 

signs and constellations of the zodiac. 



80. The Ecliptic is divided into 12 equal arcs of 30 
degrees each, called Signs, and beginning at the Vernal 
Equinox they succeed each other Eastward in the follow- 
order: Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, 
Scorpio, Sagittarius, Capricornus, Aquarius, Pisces. 

These 12 arcs of the Ecliptic are supposed to have 
corresponded about 2,200 years ago, with 12 constel- 
lations having the same rtemes. But in consequence of 



DEFINITIONS. 

the retrograde motion of the Equinoc Points, the 
Signs of the Ecliptic have left the constellations with 
which they were formerly associated. As their motion 
corresponds with that of the Equinoctial Points, they 
have moved Westward about one whole Sign in the period 
referred to, so that the division of the Ecliptic called 
Aries lies in the constellation Pisces and the Sign Taurus 
in the constellation Aries and the Sign Gemini in the con- 
stellation Taurus, &c. Hence at the present time the 
names of the constellations of the Zodiac, North of the 
Equinoctial, commencing at the Vernal Equinox, are 
Pisces, Aries, Taurus, Gemini, Cancer, Leo and continu- 
ing in the same order, those South of the same Great 
Circle, are Virgo, Libra, Scorpio, Sagittarius, Capri - 
cornus and Aquarius. — See Chart on the Base of the Lu- 
natellus Globe. 



LUNATELLUS GLOBE. 

Letters representing the principal parts of the 
JLunatellus Globe. 

A, The Arm which carries the Earth and Moon. 
F, The Semi-circle, representing the plane of the Ecliptic. 
C, The Circle of Illumination. I, The Calendar Index. 
H, The Hour Index, B, The Base. 

Q, The Quadrant. • S, The Sun. 

M, The Moon. E, The Earth. 

D, The Cap which carries the Sun. 

Directions for putting the parts together. 

ist. Place the rear end of the Arm A in the Cap D and 
tighten the screws in the Cap. Then revolve the gear in 
the Arm A with the fingers, till the central axis of the 
Globe over which we place its tubular axis, inclines di- 
rectly towards the center of the Cap D. 

2nd. Place the Cap D on the central part of the Base 
B, with the Arm A directly over the word Solstice, June 
21st, and fasten the Cap, Arm and Base together wMh the 
bolt which •ontains a thumb nut. 

3rd. Place the tubular axis of the Globe on its central 
axis which is carried by' the Arm A, so that the gear on 
the upper end of the standard, fixed in the outer end of 
the Arm A and the gear connected with the South Pole 
of the Globe, will come together; observing at the same 
time to have the outer ends of the yoke extending from 
the South Pole equally distant from the center of the 
Cap D. 



LUNATELLUS GLOBE. 

4th. Place the Hour Index on the North end of the 
tubulfrt axis of the Globe, and attach with a screw to the 
central axis of the Globe, the small metal bearing, con- 
taining a square hole in one end and a knob with a groove 
in it loosely pivoted in the other end ; observing to in- 
cline the bearing in putting it on directly away from the 
center of the Sun when it is in place, and then put the 
inner edg^of the Circle of Illumination in this groove, 
as it is being connected to the Instrument by the pivots 
of the yoke. 

5 th . Finally, place the Sun S with the Semi-circle F 
attached, at right angles with his Polar axis, on the cen- 
ter of the Cap D, and adjust the Moon Rod as the parts 
at the outer end of the Arm A suggest, and the Appara- 
tus will be ready to operate. 



I_.TJIsr^^TEIL.I-.TJS GLOBE. 

The Lunatellus Globe is the only device in existence 
which faithfully illustrates the mutual relations and various 
movements of the Sun, Earth and Moon. It is composed 
wholly of Iron Brass and Steel, except the Terrestrial 
Globe which represents the Earth, and the Chart that cov- 
ers the Base. 

BASE AND CHART. 

The Base of the Instrument is cast in one piece and 
has pla ed upon it a Chart showing how the Sun, Earth 
and Moon perform their functions, as members of the 
Solar System, every day and hour in the Year. 

The Chart contains in their proper relations, the Signs 
of the Zodiac, the months and days of the Year, the va- 
rious lengths of the Seasons, the periods when the Sun is 
fast and slow, the degrees of Celestial Longitude, the 
Perihelion, Aphelion, Solstitial and Equinoctial points, 
together with other Symbols relating to the various move- 
ments of the Apparatus. 

SUN AND SEMI-CIRCLE. 

The Sun is represented by a body composed of Brass 
and connected by one of its Poles to the gearing within. 
To the Equator of this body is attached a Semi-circle 
which, when properly adjusted represents the Plane of 
the Ecliptic. 



L U N A 1 ' E I , L U S G LOB E . 

EARTH. 

The Earth is represented by a Terrestrial Globe, twelve 
inches in diameter, and is pivoted by the South Pole to the 
gearing which gives it rotary motion. 

MOON. 

The Moon is represented by a Globe relative in size to 
that of the Terrestrial Globe, and is attached at one of its 
Poles to the outer end of a bent rod, the inner end of 
which is loosely pivoted to an upright placed on a disk 
which revolves, carrying the Moon around the Earth and 
and causing her to cross and recross the plane of the 
Ecliptic at an angle of about 5 degrees, as both Earth 
and Moon revolve around the Sun. 

CIRCLE OF ILLUMINATION. 

The Circle of Illumination is a flat Metallic Ring 
surrounding the Globe and loosely pivoted in the plane 
of the Equator, so that it is at liberty to change its posi- 
tion every moment as the Globe revolves around the Sun. 

Note. — This is the only Invention which produces this result in a 
natural way. 

CALENDAR INDEX. 

The Calendar Index is located in the Arm A that car- 
ries the Earth and Moon around the Sun, and it can be 
set in a moment by revolving the Arm, so as to point to 
any day of any month, or any day of the Year. 



LUNATELLUS GLOBE. 

QUADRANT OF ALTITUDE. 

The Quadrant of Altitude is a flexible strip of Metal 
graduated into equal parts, each corresponding in length 
to a degree on the Terrestrial Globe and bent when in 
use so as to closely fit its surface. 

GEARINCx. 

This Apparatus is operated by Brass and Steel Gear- 
wheels, some of which are inside of the case and some en- 
closed in the outer end of the Arm that carries the Earth 
and Moon around the Sun. 

UTILITY AND ECONOMY. 

The principles of Geography and the various positions, 
motions and phenomena of the Sun, Earth and Moon are 
expressed by this Instrument with such precision and accu- 
racy that more can be learned with its use in a few lessons, 
than can be learned in months without it, hence its ne- 
cessity in every School and Family. 

The Lunatellus Globe is manufactured by skillful 
Mechanics in the most sustantial manner, and an exact du- 
plicate of any part of it may be obtained at any time, by 
applying to the Patentee. 



